Construct-based Drawing

Construct-based Drawing

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By contrast, a construction-based approach builds an accurate drawing step-by-step, relying on previous knowledge: that the center of an incircle is the intersection of two angle bisectors of the triangle.

  1. Draw the triangle:

 

  1. Construct the angle bisector of one angle.
  2. Construct the angle bisector of the second angle.
  3. Construct the intersection point D of the two angle bisectors:

 

  1. Construct a line perpendicular to AC through D. Construct the point E, where the new line intersects AC:

 

  1. Draw a circle centered at D which passes through E:

 

It requires some geometric foreknowledge or ingenuity to come up with this construction, nor is it clear without a proof that the circle is indeed tangent to sides AB and BC.

Construction-based drawing is the approach used by other interactive geometry applications, and therefore you may be used to it. Constraint-based drawing, on the other hand, enables a more natural, exploratory style of problem solving. In practice, youll probably use a combination of these two approaches, making the geometry much easier to create.